Question

Dados os polinômios
A=x-2
B=x-3
C=x+1
D=x+5

Calcule:
A.B.D=
A.C.D=
A²=
B²=
C²=
D²=
A²+B²+C²+D²=
A²-B²-C²-D²=

Answer 1

A.B.D=
(x-2)(x-3)(x+5)=
(x²-3x-2x+6)(x+5)=
(x²-5x+6)(x+5)=
x³+5x²-5x²-25x+6x+30=
x³-19x+30

A.C.D=
(x-2)(x+1)(x+5)=
(x²+x-2x-2)(x+5)=
(x²-x-2)(x+5)=
x³+5x²-x²-5x-2x-10=
x³+4x²-7x-10

A²=
(x-2)²=
(x-2)(x-2)=
x²-2x-2x+4=
x²-4x+4

B²=
(x-3)²=
(x-3)(x-3)=
x²-3x-3x+9=
x²-6x+9

C²=
(x+1)²=
(x+1)(x+1)=
x²+x+x+1=
x²+2x+1

D²=
(x+5)²=
(x+5)(x+5)=
x²+5x+5x+25=
x²+10x+25

A²+B²+C²+D²=
(x²-4x+4)+(x²-6x+9)+(x²+2x+1)+(x²+10x+25)=
4x²+2x+39

A²-B²-C²-D²=
(x²-4x+4)-(x²-6x+9)-(x²+2x+1)-(x²+10x+25)=
-2x²-10x-31